15.9.2021
| Variable | TAM | brms |
|---|---|---|
| Zeit in s | 0.06 | 138 |
| Iterationen | 36 | 4000 + 4000 + X |
| Speicher in MB | 0.46 | 34.73 |
| Werte je Parameter | 3 | 4000 |
i1_easyness <- brms::ranef(fit_1d_1pl_spm, summary = FALSE)$item[,"i1",1] head(i1_easyness, n = 48) %>% round(2)
## [1] 0.89 0.54 1.20 0.36 0.57 0.67 0.97 0.55 1.29 1.18 1.71 1.68 ## [13] 2.05 1.36 1.22 1.41 1.46 1.15 -0.26 0.26 0.43 0.10 0.42 0.71 ## [25] 0.51 0.80 1.07 1.16 1.26 0.90 0.85 0.29 0.10 -0.13 0.36 0.74 ## [37] 0.20 1.10 0.82 0.28 0.01 0.38 1.09 0.94 0.24 0.13 0.27 -0.15
i1_easyness %>% birtms::plot_ppmc_distribution()
\[P\left(1|\theta_k, \beta_i\right)=\frac{\exp\left(\theta_k + \beta_i\right)}{1+\exp\left(\theta_k + \beta_i\right)}\]
\[P\left(1|\theta_k, \beta_i\right)=\frac{\exp\left(\theta_k + \beta_i\right)}{1+\exp\left(\theta_k + \beta_i\right)}\]
\[P\left(1|\theta_k, \beta_i\right)=\frac{\exp\left(\theta_k + \beta_i\right)}{1+\exp\left(\theta_k + \beta_i\right)}\]
data_spm_long <- data_spm %>%
birtms::compose_dataset(
response_columns = i1:i12)(formula1PL <- birtms::build_formula())
## response ~ 1 + (1 | person) + (1 | item)
prior_1PL <- brms::prior("normal(0, 3)", class = "sd", group = "person") +
brms::prior("normal(0, 3)", class = "sd", group = "item")fit_1d_1pl_spm <- birtms::birtm( data = data_spm_long, formula = formula1PL, prior = prior_1PL, file = "models/fit_1d_1pl_spm" )
summary(fit_1d_1pl_spm, robust = TRUE)
## Family: bernoulli ## Links: mu = logit ## Formula: response ~ 1 + (1 | person) + (1 | item) ## Data: data (Number of observations: 5988) ## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1; ## total post-warmup draws = 4000 ## ## Group-Level Effects: ## ~item (Number of levels: 12) ## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS ## sd(Intercept) 1.49 0.32 1.02 2.46 1.00 1193 2063 ## ## ~person (Number of levels: 499) ## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS ## sd(Intercept) 1.68 0.08 1.54 1.85 1.00 1561 2524 ## ## Population-Level Effects: ## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS ## Intercept 1.05 0.43 0.18 2.02 1.01 682 1213 ## ## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS ## and Tail_ESS are effective sample size measures, and Rhat is the potential ## scale reduction factor on split chains (at convergence, Rhat = 1).
bayesplot::mcmc_trace(
fit_1d_1pl_spm, pars = c("b_Intercept")
)
g_spm_2pl <- birtms::ICC_check( fit_1d_2pl_spm, post_responses = posterior_responses_spm_2pl, num_groups = 6, item_id = 12, ellipse_type = "axisparallel")
marg_loo1pl <- birtms::loo_marginal(fit_1d_1pl_spm) marg_loo2pl <- birtms::loo_marginal(fit_1d_2pl_spm)
loo::loo_compare(marg_loo1pl, marg_loo2pl)
## elpd_diff se_diff ## model2 0.0 0.0 ## model1 -25.4 11.1
ordata_1pl_spm_fullbayes %>% birtms::plot_ppmc_or_heatmap()
ordata_2pl_spm_fullbayes %>% birtms::plot_ppmc_or_heatmap()
ordata_2pl_spm_fullbayes %>%
birtms::plot_or_heatmap(
model = fit_1d_2pl_spm)ordata_2pl_spm_fullbayes %>%
birtms::plot_or_heatmap(
model = fit_1d_2pl_spm, bayesian = TRUE)
fit_1d_1pl_spm %>% birtms::plot_wrightmap(classic = FALSE)
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